Saturation thickness

The actual costs associated with a ZenoGem application vary depending on the types of contaminants present at the site, contaminant concentrations, regulatory status and cleanup requirements, waste volume, site location and accessibility, hydraulic conductivity and saturated thickness of the aquifer, and groundwater chemistry (D22728L, pp. 39, 40). 

To avoid dewatering the aquifer, constraints can be imposed on either the upper bounds of extraction rates (e.g., Rastogi 1989 Marryott et al. 1993) or the minimum saturated thickness at numerical grid cells (e.g., Ahlfeld et al. 1998). The later approach pushes the physical limits of the system by implicitly allowing the system behavior to define the upper pumping bounds. In this later approach, however, care must be taken to ensure that the optimization search procedure remains feasible with respect to the saturated thickness constraints. 

Pumping rates at the two wells shown are systematically altered and the constraint function pk for 108 plume control points is determined. The sum of squared constraint values for each set of pumping rates is shown graphically in Figures 4a and 4b for confined and unconfmed assumptions, respectively. The minimum saturated thickness at the grid cells containing the two extraction wells is also shown on Figure 4b. The optimal solution... 

Figure 4. Response surface for (a) confined and (b) un con fined assumptions for the example depicted in Figure 3. The optimal solution is indicated by the star. The minimum saturated thickness b at the wells is contoured in (b). Negative pumping rates imply extraction.

The truncated Taylor series used in equation (8) is a linear approximation that is equivalent to assuming confined conditions, which will underpredict drawdown in unconfined problems. Therefore, a safety factor must be included to reduce the upper bound on of. This is done by multiplying the upper bound on of determined by equation (9) by the ratio of minimum allowable saturated thickness to the saturated thickness at the current solution. 

Both confined and unconfined conditions are simulated, where the hydraulic conductivity is 5 m/day and the initial saturated thickness is approximately 15.4 m for the unconfined aquifer. The transmissivity for confined conditions is 77 m2/day. The design problem is to contain the two plumes depicted on the figure, with the condition that remedial wells be located on site but not located in the building. The six candidate wells shown are used as potential pumping wells and the minimum total pumping from these wells must be determined such that the two plumes are captured. 

The two contaminant plumes are represented in the first stage of the optimization formulation with a set of 110 control points along the plume boundaries. These same control point locations are used as starting points for particles when forward tracking is used in the second stage of the solution process. For the unconfined simulation, additional constraints are included to require a minimum saturated thickness of 1.5 m at each well cell. Both confined and unconfined assumptions are simulated under two sets of penalty parameters. Recall that the solution algorithm uses the penalty method for the plume capture constraints, in which each constraint violation is multiplied by a penalty parameter and added to the objective function. 

Schombel, L. F., 1994, Bedrock and alluvial aquifer saturated thickness isopach maps in Wossner, W. W., ed. Missoula, Montana, Montana Department of Justice, Natural Resource Damage Litigation Program, p. 130. 

At steady state, the principal of conservation of mass dictates that the rate at which water crosses an imaginary cylindrical boundary at a radius r from the well must be the same as the rate at which water is pumped from the well. The area of the cylindrical boundary is equal to its circumference (27rr) multiplied by its height (b), which is approximated by the saturated thickness... 

Equations [3-6], [3-7a], and [3-7b] assume that the saturated aquifer thickness b is constant (as in a confined aquifer). In unconfined (phreatic) aquifers, which are somewhat more susceptible to subsurface contamination, the saturated thickness varies as the hydraulic head changes thus b is not, strictly speaking, constant. Unless otherwise stated, however, it is assumed in the following discussions that changes in the water table height of a phreatic aquifer are relatively small compared with the saturated thickness. When this is not the case, more complex expressions are needed to describe the hydrodynamics, and the reader is referred to Bear (1979). 

Equations [3-8a] to [3-8c] are different applications of the Thiem equation, which estimates drawdown in an aquifer or well under steady-state conditions. As previously mentioned, it is assumed that the changes in saturated aquifer thickness are small compared with the total saturated depth. This is necessarily true in a confined aquifer, but not always in an unconfined (phreatic) aquifer. If drawdown becomes a significant fraction of the saturated aquifer thickness, more complicated expressions for drawdown are obtained see Bear (1979). For an unconfined aquifer in which drawdown is a significant fraction of the saturated thickness, Eq. [3-8a] must be expressed in terms of head instead of drawdown ... 

If the maximum difference in chloride concentration between ground-waters from bedrock and drift aquifers is equal to 200 mg/1 = 5.6310 mol/1 (Table I), and the distance travelled is the mean saturated thickness of the drift, or 1500 cm, and the appropriate diffusion coefficient of NaCl at 25°C is 1.576 10" cm s (Robinson and Stokes, 1955), is calculated to be 5.91 10 molcm" s . This calculation, indicates that molecular diffusion is insignificant in magnitude when compared with the velocity of groundwater. It therefore appears that mechanical mixing in the lower drift-upper bedrock aquifer is the most important cause of dispersion. 

The residuum is 47 ft thick at Piedmont Plant Farm. The water level was measured from January 1980 to September 1981, and the average residuum water level at Piedmont Plant Farm was 32.9 ft below land surface. Consequently, the average saturated thickness was 14.1 ft. Based on a saturated thickness of 14.1 ft, the estimated transmissivity of the residuum at Piedmont Plant Farm was calculated to be 0.3 ft /d. 

The residuum is 50 ft thick at Stocks Farm. Residuum water-level measurements made from January 1980 to September 1981 showed that the average residuum water level at Stocks Farm was 13.0 ft below land surface. In contrast to Piedmont Plant Farm, the average saturated thickness at Stocks Farm was 37.0 ft, which resulted in a higher estimated transmissivity. The transmissivity of the residuum at Stocks Farm was estimated to be 1,000 ft /d, based on the saturated thickness of the residuum. 

Flow Modeling. The flow component of the random walk model was used to produce the head distribution shown in Figure 3a. The hydraulic conductivity of the aquifer was set equal to 200 ft/day (61 m/day). The saturated thickness of the aquifer is equal to the elevation of the water table above the Impermeable bedrock the water table elevation is adjusted automatically during the iteration process used to solve the flow equation. 

Contaminant Transport Modeling. A major difficulty in the calibration of any two-dimensional contaminant transport model is relating the two-dimensional simulated plume to the real three-dimensional plume. A model based on Equation 4 can simulate two dimensions in cross section or areal view. An areal view was selected for the problem considered here. Use of a two-dimensional areal view model implies that the contaminant is uniformly spread out through the entire saturated thickness of the aquifer. However, in the field the aldicarb plume is only around 10 feet (3m) thick while the aquifer is around 70 feet (21 m) thick. Moreover, the concentration data were collected from wells having 3 ft (0.91 m) well screens and hence are representative of only a small fraction of the total aquifer thickness. It was decided to calibrate the model to concentrations representative of the center of the plume vertically. That is, the model was calibrated to maximum measured concentrations in each well nest. As a result, the loading rate to the model is inflated over probable field values. The model assumes the load to the model is distributed over the full aquifer thickness, when in the field the zone of maximum concentration is probably no more than 3 feet thick. Therefore, the probable loading rate in the field is roughly 3/70 or 4% of that used to calibrate the model. 

Contraction = (dry thickness - acid-saturated thickness)/dry thickness x 100%. ... 

The degree of heat utilization also depends on the presence of partings in the reservoir stratum. For steaming treatments, it is recommended that the total thickness of the reservoir bed not be more than 2-3 times the effective oil saturated thickness [18], Moreover, the thickness of the individual impermeable interlayers also has an effect on utilization of thermal energy. The interference of heat between successive permeable layers or horizons decreases when they are separated by thick impermeable interlayers. It is also reduced when heat zones shift irregularly along fingers of permeable layers. As a consequence, the overall heat effectiveness of the process suffers [18]. 

If the walls of a porous structure are subjected to a through diffusion saturation, thick (tens and hundreds of micrometers) quasi-homogeneous diffusion layers are obtained, and this method can replace epitaxy (Astrova et al. 2000). Similarly, full thermal oxidation of silicon walls makes it possible to obtain thick oxide layers, which are used, e.g., for thermal insulation purposes (Kan and Finstad 2005 Barillaro et al. 2003). The increasing volume of the oxide leads to filling of pores, which enables, at a correct choice of the porosity (<56 %), formation of a thick monolithic... 

Transmissivity A measure of the amount of water that can be transmitted horizontally through a unit width by the full saturated thickness of the aquifer under a hydraulic gradient of one. 

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